dwtbd,
And also, as John Lennon said, possession is nine-tenths of the problem!
Because desire is experienced as an internal mental event it feels as if it's ours. Buddha has something to say on this. He said that all his teachings can be summed up in one sentence and that sentence is "Nothing should be clung to as I, me or mine".
It seems that as well as giving up there's also giving. We give up drinking by giving our desire to the Beast.